Optical fibers can be used in any of a variety of different communications and sensing applications. For example, optical fiber-based acoustic sensors can be used for undersea applications. An optical fiber-based acoustic sensor can be formed by winding a length of optical fiber around a mandrel, where the fiber can be up to tens of hundreds of meters long. The sensor industry typically uses a conventional reduced-cladding fiber (80 μm diameter), which is an improvement over a standard-size (125 μm) fiber. A mode field diameter can typically be in the range of 7-10 μm, so light can be concentrated within the core region of the optical fiber and possibly a layer of a few microns of the cladding adjacent to it.
Most fiber-based acoustic sensors detect sound by determining a differential phase delay of light propagating through a length of optical fiber and the associated environmental strain placed on the fiber, as demonstrated below:
                                          Δ            ⁢                                                  ⁢            Φ                    Φ                =                              ɛ            z                    -                                                    η                2                            2                        ⁡                          [                                                                    (                                                                  P                        11                                            +                                              P                        12                                                              )                                    ⁢                                      ɛ                    r                                                  +                                                      P                    12                                    ⁢                                      ɛ                    z                                                              ]                                                          Equation        ⁢                                  ⁢        1                            Where: P11 and P12 are the elasto-optic coefficients for fused silica;        η is the refractive index of the fiber core; and        εz and εr are the longitudinal and radial strains, respectively.Alternatively, Equation 1 can be expressed explicitly as a function of fiber length and radius, as demonstrated below:        
                                          Δ            ⁢                                                  ⁢            Φ                    Φ                =                                            Δ              ⁢                                                          ⁢              L                        L                    -                                                    η                2                            2                        ⁡                          [                                                                    (                                                                  P                        11                                            +                                              P                        12                                                              )                                    ⁢                                                            Δ                      ⁢                                                                                          ⁢                      r                                        r                                                  +                                                      P                    12                                    ⁢                                                            Δ                      ⁢                                                                                          ⁢                      L                                        L                                                              ]                                                          Equation        ⁢                                  ⁢        2                            Where: L is the fiber length; and        r is the fiber radius.In the first order, the phase shift is dominated by the axial strain, and the radial component can thus be ignored. Therefore, Equation 2 can be rewritten as follows:        
                                          Δ            ⁢                                                  ⁢            Φ                    Φ                =                                            Δ              ⁢                                                          ⁢              L                        L                    ⁢                      (                          1              -                                                                    η                    2                                    2                                ⁢                                  P                  12                                                      )                                              Equation        ⁢                                  ⁢        3            
Based on Equations 1-3, it is demonstrated that, to increase phase shift, one can change the elasto-optic coefficient, increase an amount of strain per unit length experienced by the fiber, or increase the fiber length. However, the elasto-optic coefficient is a material property and is considered to be invariant. In addition, the amount of strain per unit length is governed by the transduction of force to the fused silica base material. Furthermore, increasing the fiber length may be impractical from a design, manufacturing, and cost perspective.